Preheat oven to 400°F. Lightly butter a deep round or oval 8- or 9-inch oven-safe casserole dish.
Peel and thinly slice potatoes into ¼-inch thickness using mandoline or sharp knife, reserving end slices for another use. Place potatoes in large bowl.
In another bowl, stir together cheddar, Parmesan, onion powder, garlic powder, paprika, salt and pepper, tossing to combine. Stir in cream and milk. Pour over potatoes; using your hands, separate and evenly coat slices with the mixture.
Pick up potatoes and, being sure to get some cheese in between, stack edges upright in a tight concentric circle – like dominos – in prepared dish. Fill in centre with remaining slices; pour over any remaining cream mixture.
Drizzle top with melted butter. Cover tightly with foil, then place on a baking sheet. Bake for 1 hour; uncover and bake until top is golden and crispy, 25 to 30 minutes. Let stand for 10 minutes before serving.